On unicyclic graphs of metric dimension 2 with vertices of degree 4

We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constr...

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Published in:Algebra and Discrete Mathematics
Date:2018
Main Authors: Dudenko, M., Oliynyk, B.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2018
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/188412
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Dudenko, M.
Oliynyk, B.
author_facet Dudenko, M.
Oliynyk, B.
citation_txt On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-11-25T21:04:25Z
publishDate 2018
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Dudenko, M.
Oliynyk, B.
2023-02-27T16:01:35Z
2023-02-27T16:01:35Z
2018
On unicyclic graphs of metric dimension 2 with vertices of degree 4 / M. Dudenko, B. Oliynyk // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 256–269. — Бібліогр.: 13 назв. — англ.
1726-3255
2010 MSC: 05C12.
https://nasplib.isofts.kiev.ua/handle/123456789/188412
We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized.
The authors thank to the International Charitable Foundation for Renaissance of the Kyiv-Mohyla Academy for the financial support of their research.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
On unicyclic graphs of metric dimension 2 with vertices of degree 4
Article
published earlier
spellingShingle On unicyclic graphs of metric dimension 2 with vertices of degree 4
Dudenko, M.
Oliynyk, B.
title On unicyclic graphs of metric dimension 2 with vertices of degree 4
title_full On unicyclic graphs of metric dimension 2 with vertices of degree 4
title_fullStr On unicyclic graphs of metric dimension 2 with vertices of degree 4
title_full_unstemmed On unicyclic graphs of metric dimension 2 with vertices of degree 4
title_short On unicyclic graphs of metric dimension 2 with vertices of degree 4
title_sort on unicyclic graphs of metric dimension 2 with vertices of degree 4
url https://nasplib.isofts.kiev.ua/handle/123456789/188412
work_keys_str_mv AT dudenkom onunicyclicgraphsofmetricdimension2withverticesofdegree4
AT oliynykb onunicyclicgraphsofmetricdimension2withverticesofdegree4